U.S. President Barack Obama hopes to get a climate change bill on his desk this year and is open to discussing how stringent the rules of a carbon emissions trading system should be for industry, a top adviser said on Tuesday.

Nancy Sutley, chairwoman of the White House Council on Environmental Quality, said the Obama administration was still studying the main climate bill in the U.S. Congress and would look at other proposals that may crop up in the coming months.

The president asked for a bill to be sent to him this year and that's, I think, still the hope, she told Reuters in an interview.

U.S. Representatives Edward Markey and Henry Waxman, both Democrats, introduced a bill in March that would cut U.S. emissions of carbon dioxide (CO2), a greenhouse gas linked to climate change, by 20 percent through 2020.

The Waxman-Markey bill would achieve that with a cap-and-trade system, which would limit the amount of CO2 that power plants or industrial users could emit. Those who cut their emissions below their allotment could sell their unused credits.

Sutley said the White House was still evaluating the bill and looking forward to working through the legislative process.

She said the administration was open to negotiating what percentage of permits in the cap and trade system should be sold or auctioned to industry.

I think it's an area for discussion, she said when asked about Obama's flexibility on his demand, articulated during the presidential campaign, for 100 percent auctioning.

She said the administration had not reached a bottom line on that issue.

Obama has indicated to business leaders that he could be flexible on the 100 percent pledge, though the White House has said he would continue to press lawmakers for that goal.

The White House has put energy reform at the top of its to-do list along with healthcare and education.

But the U.S. Senate rejected an effort to put climate change legislation on a fast track using the federal budget, making it harder for Congress to put a cap on greenhouse gas emissions this year.

The administration plans to have a cap and trade system in place by 2012, but Sutley said it was too early to say when that system could link up with an already-established one in the European Union.

EU officials are eager to have a U.S. system in place so the European scheme could expand and establish an international carbon market.

Sutley said Obama's commitment to cutting U.S. greenhouse gas emissions, which contrasted with his predecessor, former President George W. Bush, had created a different dynamic in international talks to forge a global climate pact.

Going into it, the difference is the U.S. wants to do something, she said. That's a big new thing for the international discussions.

(Editing by Eric Beech)